# Scaling and Resizing Symmetry in Feedforward Networks

arXiv: https://arxiv.org/abs/2306.15015 · HTML: https://mlsanity.com/paper/2306.15015/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 26 Jun 2023.

## Builds on (most cited first, 13 of 13)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Deep Speech: Scaling up end-to-end speech recognition](https://mlsanity.com/paper/1412.5567/) (2014)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Exponential expressivity in deep neural networks through transient chaos](https://mlsanity.com/paper/1606.05340/) (2016)
- [Dynamical Isometry and a Mean Field Theory of CNNs: How to Train 10,000-Layer Vanilla Convolutional Neural Networks](https://mlsanity.com/paper/1806.05393/) (2018)
- [The jamming transition as a paradigm to understand the loss landscape of deep neural networks](https://mlsanity.com/paper/1809.09349/) (2018)
- [Dynamical Isometry and a Mean Field Theory of RNNs: Gating Enables Signal Propagation in Recurrent Neural Networks](https://mlsanity.com/paper/1806.05394/) (2018)
- [Deep Learning Models of the Retinal Response to Natural Scenes](https://mlsanity.com/paper/1702.01825/) (2017)
- [A Correspondence Between Random Neural Networks and Statistical Field Theory](https://mlsanity.com/paper/1710.06570/) (2017)
- [Exact Phase Transitions in Deep Learning](https://mlsanity.com/paper/2205.12510/) (2022)

## Abstract (arXiv)

Weights initialization in deep neural networks have a strong impact on the speed of converge of the learning map. Recent studies have shown that in the case of random initializations, a chaos/order phase transition occur in the space of variances of random weights and biases. Experiments then had shown that large improvements can be made, in terms of the training speed, if a neural network is initialized on values along the critical line of such phase transition. In this contribution, we show evidence that the scaling property exhibited by physical systems at criticality, is also present in untrained feedforward networks with random weights initialization at the critical line. Additionally, we suggest an additional data-resizing symmetry, which is directly inherited from the scaling symmetry at criticality.